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AMO 2027 Grades 9-11 SET 2 - Self-study Question 12

AMO · AMO 2027 Grades 9-11 SET 2 - Self-study

Question 12

Find the positive difference between the sum of all possible integer $x$ values and the sum of all possible integer $y$ values satisfying $x^y=256$.
Use the source's convention: sum the $x$-coordinates and the $y$-coordinates over all distinct ordered solution pairs $(x,y)$, counting a repeated coordinate once for each pair in which it appears.

Choose one option.
  1. 16
  2. 227
  3. 32
  4. 29
  5. 256